The \(K^\pm _{l3}\)  decays are modelled according to [1]} including both the Dalitz plot density of Eq. (REF ) and radiative corrections, with exactly one photon emitted in each decay, and tracked through the detector if its energy in the laboratory frame is above 1 MeV.
This approach takes into account the infrared divergence of photon radiation by extending the soft-photon approximation [2]} to the whole energy range.
The implementation has been validated in [1]} using the experimental data available at the time [4]}, [5]}: photon energy and photon-lepton angle distributions have been found to agree with the data within 1–5% systematic uncertainty. However this uncertainty includes the effect of a 100% variation of the vector FF slope. Therefore the distributions considered are not sensitive to the FF description at the level of precision required for the present study.
